Introduction to Syntax and Context-Free Grammars

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Introduction to Syntax andContext-Free Grammars

• Owen Rambow
• rambow_at_cs.columbia.edu
• September 26 2006

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What is Syntax?

• Study of structure of language
• Roughly, goal is to relate surface form (what we
  perceive when someone says something) to
  semantics (what that utterance means)

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What is Syntax Not?

• Phonology study of sound systems and how sounds
  combine
• Morphology study of how words are formed from
  smaller parts (morphemes)
• Semantics study of meaning of language

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What is Syntax? (2)

• Study of structure of language
• Specifically, goal is to relate an interface to
  morphological component to an interface to a
  semantic component
• Note interface to morphological component may
  look like written text
• Representational device is tree structure

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Simplified View of Linguistics
Phonology
? /waddyasai/
Morphology
/waddyasai/ ? what did you say
say
Syntax
what did you say ?
obj
subj
what
you
say
Semantics
obj
subj
? P ?x. say(you, x)
what
you
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The Big Picture
Empirical Matter
?

• Formalisms
• Data structures
• Formalisms (e.g., CFG)
• Algorithms
• Distributional Models

?
Maud expects there to be a riot Teri promised
there to be a riot Maud expects the shit to hit
the fan Teri promised the shit to hit the fan
?
?
Linguistic Theory
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What About Chomsky?

• At birth of formal language theory (comp sci) and
  formal linguistics
• Major contribution syntax is cognitive reality
• Humans able to learn languages quickly, but not
  all languages ? universal grammar is biological
• Goal of syntactic study find universal
  principles and language-specific parameters
• Specific Chomskyan theories change regularly
• General ideas adopted by almost all contemporary
  syntactic theories (principles-and-parameters-typ
  e theories)

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Types of Linguistic Theories

• Descriptive provide account of syntax of a
  language often appropriate for NLP engineering
  work
• Explanatory provide principles-and-parameters
  style account of syntax of (preferably) several
  languages
• Prescriptive prescriptive linguistics is an
  oxymoron

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The Big Picture
Empirical Matter

• Formalisms
• Data structures
• Formalisms
• Algorithms
• Distributional Models

?
Maud expects there to be a riot Teri promised
there to be a riot Maud expects the shit to hit
the fan Teri promised the shit to hit the
?
?
Linguistic Theory
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Structure in Strings

• Some words the a small nice big very boy girl
  sees likes
• Some good sentences
• the boy likes a girl
• the small girl likes the big girl
• a very small nice boy sees a very nice boy
• Some bad sentences
• the boy the girl
• small boy likes nice girl
• Can we find subsequences of words (constituents)
  which in some way behave alike?

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Structure in StringsProposal 1

• Some words the a small nice big very boy girl
  sees likes
• Some good sentences
• (the) boy (likes a girl)
• (the small) girl (likes the big girl)
• (a very small nice) boy (sees a very nice boy)
• Some bad sentences
• (the) boy (the girl)
• (small) boy (likes the nice girl)

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Structure in StringsProposal 2

• Some words the a small nice big very boy girl
  sees likes
• Some good sentences
• (the boy) likes (a girl)
• (the small girl) likes (the big girl)
• (a very small nice boy) sees (a very nice boy)
• Some bad sentences
• (the boy) (the girl)
• (small boy) likes (the nice girl)

• This is better proposal fewer types of
  constituents
• (blue and red are of same type)

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More Structure in StringsProposal 2 -- ctd

• Some words the a small nice big very boy girl
  sees likes
• Some good sentences
• ((the) boy) likes ((a) girl)
• ((the) (small) girl) likes ((the) (big) girl)
• ((a) ((very) small) (nice) boy) sees ((a) ((very)
  nice) girl)
• Some bad sentences
• ((the) boy) ((the) girl)
• ((small) boy) likes ((the) (nice) girl)

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From Substrings to Trees

• (((the) boy) likes ((a) girl))

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Node Labels?

• ( ((the) boy) likes ((a) girl) )
• Choose constituents so each one has one
  non-bracketed word the head
• Group words by distribution of constituents they
  head (part-of-speech, POS)
• Noun (N), verb (V), adjective (Adj), adverb
  (Adv), determiner (Det)
• Category of constituent XP, where X is POS
• NP, S, AdjP, AdvP, DetP

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Node Labels

• (((the/Det) boy/N) likes/V ((a/Det) girl/N))

S
likes
NP
NP
boy
girl
DetP
DetP
a
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Types of Nodes

• (((the/Det) boy/N) likes/V ((a/Det) girl/N))

Phrase-structure tree
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Determining Part-of-Speech

• A blue seat/a child seat noun or adjective?
• Syntax
• a blue seat a child seat
• a very blue seat a very child seat
• this seat is blue this seat is child
• Morphology
• bluer childer
• blue and child are not the same POS
• blue is Adj, child is Noun

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Determining Part-of-Speech (2)

• preposition or particle?
• A he threw out the garbage
• B he threw the garbage out the door
• A he threw the garbage out
• B he threw the garbage the door out
• The two out are not same POS A is particle, B is
  Preposition

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Word Classes (POS)

• Heads of constituents fall into distributionally
  defined classes
• Additional support for class definition of word
  class comes from morphology

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Some Points on POS Tag Sets

• Possible basic set N, V, Adj, Adv, P, Det, Aux,
  Comp, Conj
• 2 supertypes open- and closed-class
• Open N, V, Adj, Adv
• Closed P, Det, Aux, Comp, Conj
• Many subtypes
• eat/V ? eat/VB, eat/VBP, eats/VBZ, ate/VBD,
  eaten/VBN, eating/VBG,
• Reflect morphological form syntactic function

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Phrase Structure and Dependency Structure
All nodes are labeled with words!
Only leaf nodes labeled with words!
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Phrase Structure and Dependency Structure (ctd)
Representationally equivalent if each
nonterminal node has one lexical daughter (its
head)
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Types of Dependency
Adj(unct)
Obj
Subj
Fw
Fw
Adj
Adj
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Grammatical Relations

• Types of relations between words
• Arguments subject, object, indirect object,
  prepositional object
• Adjuncts temporal, locative, causal, manner,
• Function Words

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Subcategorization

• List of arguments of a word (typically, a verb),
  with features about realization (POS, perhaps
  case, verb form etc)
• In canonical order Subject-Object-IndObj
• Example
• like N-N, N-V(to-inf)
• see N, N-N, N-N-V(inf)
• Note JM talk about subcategorization only
  within VP

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What About the VP?
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What About the VP?

• Existence of VP is a linguistic (i.e., empirical)
  claim, not a methodological claim
• Semantic evidence???
• Syntactic evidence
• VP-fronting (and quickly clean the carpet he did!
  )
• VP-ellipsis (He cleaned the carpets quickly, and
  so did she )
• Can have adjuncts before and after VP, but not in
  VP (He often eats beans, he eats often beans )
• Note VP cannot be represented in a dependency
  representation

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Context-Free Grammars

• Defined in formal language theory (comp sci)
• Terminals, nonterminals, start symbol, rules
• String-rewriting system
• Start with start symbol, rewrite using rules,
  done when only terminals left
• NOT A LINGUISTIC THEORY, just a formal device

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CFG Example

• Many possible CFGs for English, here is an
  example (fragment)
• S ? NP VP
• VP ? V NP
• NP ? DetP N AdjP NP
• AdjP ? Adj Adv AdjP
• N ? boy girl
• V ? sees likes
• Adj ? big small
• Adv ? very
• DetP ? a the

the very small boy likes a girl
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Derivations in a CFG
S

• S ? NP VP
• VP ? V NP
• NP ? DetP N AdjP NP
• AdjP ? Adj Adv AdjP
• N ? boy girl
• V ? sees likes
• Adj ? big small
• Adv ? very
• DetP ? a the

S
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Derivations in a CFG
NP VP

• S ? NP VP
• VP ? V NP
• NP ? DetP N AdjP NP
• AdjP ? Adj Adv AdjP
• N ? boy girl
• V ? sees likes
• Adj ? big small
• Adv ? very
• DetP ? a the

S
NP
VP
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Derivations in a CFG
DetP N VP

• S ? NP VP
• VP ? V NP
• NP ? DetP N AdjP NP
• AdjP ? Adj Adv AdjP
• N ? boy girl
• V ? sees likes
• Adj ? big small
• Adv ? very
• DetP ? a the

S
NP
VP
DetP
N
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Derivations in a CFG
the boy VP

• S ? NP VP
• VP ? V NP
• NP ? DetP N AdjP NP
• AdjP ? Adj Adv AdjP
• N ? boy girl
• V ? sees likes
• Adj ? big small
• Adv ? very
• DetP ? a the

S
NP
VP
DetP
N
boy
the
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Derivations in a CFG
the boy likes NP

• S ? NP VP
• VP ? V NP
• NP ? DetP N AdjP NP
• AdjP ? Adj Adv AdjP
• N ? boy girl
• V ? sees likes
• Adj ? big small
• Adv ? very
• DetP ? a the

S
NP
VP
DetP
N
V
NP
boy
the
likes
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Derivations in a CFG
the boy likes a girl

• S ? NP VP
• VP ? V NP
• NP ? DetP N AdjP NP
• AdjP ? Adj Adv AdjP
• N ? boy girl
• V ? sees likes
• Adj ? big small
• Adv ? very
• DetP ? a the

S
NP
VP
DetP
N
V
NP
boy
the
likes
N
DetP
girl
a
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Derivations in a CFGOrder of Derivation
Irrelevant
NP likes DetP girl

• S ? NP VP
• VP ? V NP
• NP ? DetP N AdjP NP
• AdjP ? Adj Adv AdjP
• N ? boy girl
• V ? sees likes
• Adj ? big small
• Adv ? very
• DetP ? a the

S
NP
VP
V
NP
likes
N
DetP
girl
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Derivations of CFGs

• String rewriting system we derive a string
  (derived structure)
• But derivation history represented by
  phrase-structure tree (derivation structure)!

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Formal Definition of a CFG

• G (V,T,P,S)
• V finite set of nonterminal symbols
• T finite set of terminal symbols, V and T are
  disjoint
• P finite set of productions of the form
• A ? ?, A ? V and ? ? (T ? V)
• S ? V start symbol

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Grammar Equivalence

• Can have different grammars that generate same
  set of strings (weak equivalence)
• Grammar 1 NP ? DetP N and DetP ? a the
• Grammar 2 NP ? a N NP ? the N
• Can have different grammars that have same set of
  derivation trees (strong equivalence)
• With CFGs, possible only with useless rules
• Grammar 2 NP ? a N NP ? the N
• Grammar 3 NP ? a N NP ? the N, DetP ? many
• Strong equivalence implies weak equivalence

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Normal Forms c

• There are weakly equivalent normal forms (Chomsky
  Normal Form, Greibach Normal Form)
• There are ways to eliminate useless productions
  and so on see your formal language textbook

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Chomsky Normal Form

• A CFG is in Chomsky Normal Form (CNF) if all
  productions are of one of two forms
• A ? BC with A, B, C nonterminals
• A ? a, with A a nonterminal and a a terminal
• Every CFG has a weakly equivalent CFG in CNF

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Generative Grammar

• Formal languages formal device to generate a set
  of strings (such as a CFG)
• Linguistics (Chomskyan linguistics in
  particular) approach in which a linguistic
  theory enumerates all possible strings/structures
  in a language (competence)
• Chomskyan theories do not really use formal
  devices they use CFG informally defined
  transformations

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Nobody Uses Simple CFGs (Except Intro NLP Courses)

• All major syntactic theories (Chomsky, LFG, HPSG,
  TAG-based theories) represent both phrase
  structure and dependency, in one way or another
• All successful parsers currently use statistics
  about phrase structure and about dependency
• Derive dependency through head percolation for
  each rule, say which daughter is head

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Massive Ambiguity of Syntax

• For a standard sentence, and a grammar with wide
  coverage, there are 1000s of derivations!
• Example
• The large portrait painter told the delegation
  that he sent money orders in a letter on Wednesday

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Penn Treebank (PTB)

• Syntactically annotated corpus of newspaper texts
  (phrase structure)
• The newspaper texts are naturally occurring data,
  but the PTB is not!
• PTB annotation represents a particular linguistic
  theory (but a fairly vanilla one)
• Particularities
• Very indirect representation of grammatical
  relations (need for head percolation tables)
• Completely flat structure in NP (brown bag lunch,
  pink-and-yellow child seat )
• Has flat Ss, flat VPs

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Example from PTB

• ( (S (NP-SBJ It)
• (VP 's
• (NP-PRD (NP (NP the latest investment
  craze)
• (VP sweeping
• (NP Wall Street)))
• (NP (NP a rash)
• (PP of
• (NP (NP new closed-end country funds)
• ,
• (NP (NP those
• (ADJP publicly traded)
• portfolios)
• (SBAR (WHNP-37 that)
• (S (NP-SBJ T-37)
• (VP invest
• (PP-CLR in
• (NP (NP stocks)
• (PP of

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Types of syntactic constructions

• Is this the same construction?
• An elf decided to clean the kitchen
• An elf seemed to clean the kitchen
• An elf cleaned the kitchen
• Is this the same construction?
• An elf decided to be in the kitchen
• An elf seemed to be in the kitchen
• An elf was in the kitchen

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Types of syntactic constructions (ctd)

• Is this the same construction?
• There is an elf in the kitchen
• There decided to be an elf in the kitchen
• There seemed to be an elf in the kitchen
• Is this the same construction?It is raining/it
  rains
• ??It decided to rain/be raining
• It seemed to rain/be raining

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Types of syntactic constructions (ctd)

• Conclusion
• to seem whatever is embedded surface subject can
  appear in upper clause
• to decide only full nouns that are referential
  can appear in upper clause
• Two types of verbs

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Types of syntactic constructions Analysis
S
S
NP
VP
VP
an elf
S
S
V
V
NP
VP
NP
VP
to decide
to seem
an elf
an elf
PP
PP
V
V
to be
to be
in the kitchen
in the kitchen
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Types of syntactic constructions Analysis
S
VP
an elf
S
V
NP
VP
seemed
an elf
PP
V
to be
in the kitchen
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Types of syntactic constructions Analysis
S
VP
an elf
S
V
NP
VP
seemed
an elf
PP
V
to be
in the kitchen
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Types of syntactic constructions Analysis
S
NPi
VP
an elf
an elf
S
V
NP
VP
seemed
ti
PP
V
to be
in the kitchen
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Types of syntactic constructions Analysis

• to seem lower surface subject raises to
• upper clause raising verb
• seems (there to be an elf in the kitchen)
• there seems (t to be an elf in the kitchen)
• it seems (there is an elf in the kitchen)

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Types of syntactic constructions Analysis (ctd)

• to decide subject is in upper clause and
  co-refers with an empty subject in lower clause
  control verb
• an elf decided (an elf to clean the kitchen)
• an elf decided (PRO to clean the kitchen)
• an elf decided (he cleans/should clean the
  kitchen)
• it decided (an elf cleans/should clean the
  kitchen)

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Lessons Learned from the Raising/Control Issue

• Use distribution of data to group phenomena into
  classes
• Use different underlying structure as basis for
  explanations
• Allow things to move around from underlying
  structure -gt transformational grammar
• Check whether explanation you give makes
  predictions

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Examples from PTB

• (S (NP-SBJ-1 The ropes)
• (VP seem
• (S (NP-SBJ -1)
• (VP to
• (VP make
• (NP much sound))))))
• (S (NP-SBJ-1 The ancient church vicar)
• (VP refuses
• (S (NP-SBJ -1)
• (VP to
• (VP talk
• (PP-CLR about
• (NP it)))))

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The Big Picture
Empirical Matter
or

• Formalisms
• Data structures
• Formalisms
• Algorithms
• Distributional Models

Maud expects there to be a riot Teri promised
there to be a riot Maud expects the shit to hit
the fan Teri promised the shit to hit the
descriptive theory is about
predicts
uses
explanatory theory is about

• Linguistic Theory
• Content Relate morphology to semantics
• Surface representation (eg, ps)
• Deep representation (eg, dep)
• Correspondence